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DCG
2007
13 years 7 months ago
2007
Motivated by Gauss’s first proof of the Fundamental Theorem of Algebra, we study the topology of harmonic algebraic curves. By the maximum principle, a harmonic curve has no bou...
DCG
2007
13 years 7 months ago
2007
G. Wegner [12] gave a geometric characterization of all so–called Groemer packing of n ≥ 2 unit discs in E2 that are densest packings of n unit discs with respect to the conve...
DCG
2007
13 years 7 months ago
2007
We establish a new lower bound for the number of sides required for the component curves of simple Venn diagrams made from polygons. Specifically, for any n-Venn diagram of conve...
DCG
2007
13 years 7 months ago
2007
In this paper we investigate the Erd¨os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We pr...
DCG
2007
13 years 7 months ago
2007
We consider polytopes in Rn that are generated by N vectors in Rn whose coordinates are independent subgaussian random variables. (A particular case of such polytopes are symmetri...